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Beliebt Rechnen >

(\partial)/(\partial x)(ln(x+sqrt(y)))

Lösung

\frac{\partial}{\partial x} (ln (x + y))

Lösung

\frac{1}{x + y}

Schritte zur Lösung

\frac{\partial}{\partial x} (ln (x + y))

Behandle

y

als Konstante

Wende die Kettenregel an:

\frac{1}{x + y} \frac{\partial}{\partial x} (x + y)

= \frac{1}{x + y} \frac{\partial}{\partial x} (x + y)

\frac{\partial}{\partial x} (x + y) = 1

= \frac{1}{x + y} \cdot 1

Vereinfache

= \frac{1}{x + y}

Beliebte Beispiele

y^{^{'}} = e^{(y - x)}

((q^4)/4+(2q^3)/3-(11q^2)/2+12q)^'

(\frac{q ^{4}}{4} + \frac{2 q ^{3}}{3} - \frac{11 q ^{2}}{2} + 12 q)^{^{'}}

4(1+x^2)(dy)/(dx)=2xy(y^4-1)

4 (1 + x^{2}) \frac{d y}{d x} = 2 x y (y^{4} - 1)

derivative f(x)= 3/4 x

d er i v a t i v e f (x) = \frac{3}{4} x

derivative f(x)=(arctan(8x))^2

d er i v a t i v e f (x) = (arctan (8 x))^{2}